Matrix cracking and delamination in laminated composites. Part I: Ply constitutive law, first ply failure and onset of delamination

Matrix cracking and delamination are the main initial forms of damage in advanced laminated composites manufactured by stacking unidirectional plies of fiber reinforced polymers. In this paper, the onset of matrix cracking is determined for in-plane stress states; in addition, delamination promoted by matrix cracks is analyzed. Taking into account that under in-plane shear stresses composite laminates show a non-linear response prior to the formation of a macro-crack, a plastic-damage model is proposed and implemented. The models predictions correlate well with published experimental data.     

Interaction between matrix cracking and edge delamination in composite laminates

Matrix cracking and edge delamination are two main damage modes in continuous-fibre composite laminates. They are often investigated separately, and so the interaction between two damage modes has not yet been revealed. In this paper, a simple parallel-spring model is introduced to model the longitudinal stiffness reduction due to matrix cracking and edge delamination together. The energy release rate of edge delamination eliminating the matrix crack effect and the energy release rate of matrix cracking in the presence of edge delamination are then obtained. Experimental materials include carbon- and glass-fibre-reinforced bismaleimide composite laminates under static tension. The growth of matrix cracks and edge delaminations was recorded by means of NDT techniques. Results show that matrix cracks may initiate before or after edge lamination. This depends on the laminate layup, and especially on the thickness of the 90° plies. Edge delamination may also induce matrix cracking. Matrix cracking has a significant effect on the stiffness reduction in GRP laminates. The present model can predict the stiffness reduction in a laminate containing both matrix cracks and edge delaminations. The mixed-mode delamination fracture toughness obtained from the present model shows up to 50% differences compared with O'Brien's model for GRP laminates. However, matrix cracking has a small effect on the mixed-mode interlaminar fracture toughness of the CFRP laminates.     

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates

A variational approach is used to model the behaviour of composite cross-ply laminates damaged by transverse, longitudinal cracking and delamination. An energetic criterion is proposed. It is based on the strain energy release rate associated with each of the three damage modes. The first part of this paper is concerned with the modelling of the transverse and longitudinal cracking. In the second part, a model for studying delamination damage is presented. The numerical results show that these models provide a consistent level of accuracy for a variety of thin laminate material systems and configurations, with various combinations of delaminations and matrix cracks. In this paper several numerical simulations meant to describe initiation for each damage mode are proposed. The estimation of damage modes contributions is achieved for two thin laminates in order to predict the evolution of damage mode transition.     

Mesh-independent modeling of both distributed and discrete matrix cracking in interaction with delamination in composites

A finite element model is presented for failure analysis of composite laminates with the phantom node method for matrix cracking and interface elements for delamination. The phantom node method allows for mesh-independent representation of straight intraply cracks in laminates. In laminates two different phenomena that both involve such cracks are distinguished, namely distributed matrix cracking and discrete splitting, where the transition between the two is related to delamination. It is investigated how both phenomena and their transition can be represented in a single computational framework. Objectivity of the results with respect to element size and the introduced crack spacing parameter is examined.     

A generalized micromechanical approach for the analysis of transverse crack and induced delamination in composite laminates

The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90]_s, [45/−45]_s, [30/−30]_s and [90/45/0/−45]_s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed.     

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.     

Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates

In previous papers the microscopic failure process of (0/90_n/0) (n = 4,8,12) cross-ply laminates was investigated. Progressive damage parameters, such as the transverse crack density and the delamination ratio, were measured. A simple modified shear-lag analysis including the thermal residual strains was conducted to predict the transverse crack density and the delamination length. The analysis did not consider the interaction between the transverse cracks and the delamination. In the present paper, a prediction is presented for the transverse crack density including the effect of delamination growth. The prediction shows better agreement with the experimental results, especially for laminates with thicker 90 ° plies in which extensive delamination occurs.

Loading/unloading tests have also been performed to obtain the Young's modulus reduction and the permanent strain as functions of the damage state. The shear-lag predictions of the Young's modulus reduction and the permanent strain are compared with the experimental data. Better agreement is obtained when the interaction between transverse cracks and delamination is considered.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 cycles (Initiation and propagation of delamination considering interaction with transverse cracks)

High-cycle fatigue features of over 10⁸ cycles, particularly the initiation and propagation of edge delamination considering the effects of transverse cracks, were investigated using quasi-isotropic carbon-fiber-reinforced plastic (CFRP) laminates with a stacking sequence of [45/0/−45/90]_s in this study. In the relationship between a transverse crack density and initiation and growth of edge delamination, it was found that fatigue damage growth behavior varied depending on applied stress. It was observed that edge delamination initiated and grew at parts where transverse cracks were dense at ordinary applied stress, whereas it was observed that edge delamination grew before or simultaneously with transverse crack propagation at a low applied stress and high-cycle loading. In addition, the critical transverse crack density where delamination begins growing was calculated to evaluate the interaction between transverse crack and edge delamination growth.     

Mesh‐independent matrix cracking and delamination modeling in laminated composites

The initiation and evolution of transverse matrix cracks and delaminations are predicted within a mesh‐independent cracking (MIC) framework. MIC is a regularized extended finite element method (x‐FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra‐ply MIC opening is implemented by using a mixed‐mode cohesive formulation in a fully three‐dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates withouttextita priori knowledge of damage location or initiation. Good agreement with conventional numerical solutions and/or experimental data was observed in all the problems considered. Published 2011. This article is a US Government work and is in the public domain in the USA.     

Tension fatigue analysis and life prediction for composite laminates

A tension fatigue life prediction methodology for composite laminates is presented. Tension fatigue tests were conducted on quasi-isotropic and orthotropic glass epoxy, graphite epoxy, and glass/graphite epoxy hybrid laminates. Edge delamination onset data were used to generate plots of strain energy release rate as a function of cycles to delamination onset. These plots were then used along with strain energy release rate analyses of delaminations initiating at matrix cracks to predict local delamination onset. Stiffness loss was measured experimentally to account for the accumulation of matrix cracks and for delimination growth. Fatigue failure was predicted by comparing the increase in global strain resulting from stiffness loss to the decrease in laminate failure strain resulting from delaminations forming at matrix cracks through the laminate thickness. Good agreement between measured and predicted lives indicated that the through-thickness damage accumulation model can accurately describe fatigue failure for laminates where the delamination onset behaviour in fatigue is well characterized, and stiffness loss can be monitored in real time to account for damage growth.     

一种改进的内聚力损伤模型在复合材料层合板低速冲击损伤模拟中的应用

针对传统内聚力损伤模型(CZM)无法考虑层内裂纹对界面分层影响的缺点,提出了一种改进的适用于复合材料层合板低速冲击损伤模拟的CZM。通过对界面单元内聚力本构模型中的损伤起始准则进行修正,考虑了界面层相邻铺层内基体、纤维的损伤状态及应力分布对层间强度和分层扩展的影响。基于ABAQUS用户子程序VUMAT,结合本文模型及层合板失效判据,建立了模拟复合材料层合板在低速冲击作用下的渐进损伤过程的有限元模型,计算了不同铺层角度和材料属性的层合板在低速冲击作用下的损伤状态。通过数值模拟与试验结果的对比,验证了本文方法的精度及合理性。     

Analysis of composite skin/stiffener debounding and failure under uniaxial loading

In this paper, damage mechanisms in the composite bounded skin/stiffener constructions under monotonic tension loading are investigated. The approach uses experiments to detect the failure mechanisms, two and three-dimensional stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for cracks and delamination growth. The laminates strength and damage mechanisms obtained from both experimental and finite elements analysis are presented for several laminates lay-up configurations. Observations on the performed experiments show matrix crack initiation and propagation in the skin and near the flange tip, causing the flange to almost fully debounded from the skin in some cases, interlaminar debounding and fiber breakage up to the failure of the components. The finite elements analysis is also show that the matrix cracks are initiated in the first skin layer for most of the cases. With increasing the applied load the matrix cracks are propagated through the thickness to reach the next layer and causes delamination between the two layers. With increasing the applied load this delamination is propagated up to the occurrence of unstable delamination growth or the first fiber breakage known as the final failure of the component. The obtained experimental failure loads are compared with those calculated by the finite elements analysis.     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.     

Modeling delamination migration in cross-ply tape laminates

A novel modeling approach is proposed that combines the Floating Node Method (FNM) with the Virtual Crack Closure Technique (VCCT) to capture delamination migration in cross-ply tape laminates. Delamination migration is the damage process by which a delamination propagating at an interface relocates to a different interface via one or multiple matrix cracks. In the approach proposed, delamination, matrix cracking, and their interaction, are represented in a single element. The kinematics of both delamination and matrix cracks are represented explicitly. Migration onset location, and subsequent path, are determined as part of the solution, in a mesh-independent fashion. Delamination growth, matrix cracking, and migration onset, are all modeled using fracture mechanics based failure and migration criteria. The proposed approach is applied to the modeling of the Delamination Migration (DM) test, showing good qualitative and quantitative agreement with experiments.     

Stiffness properties of composite laminates with matrix cracking and interior delamination

Two modes of damage in composite laminates are considered: the intralaminar damage (matrix cracking) and the interlaminar damage (interior delamination). Using a vectorial representation of damage as internal variables in a phenomenological theory, relationships between the overall stiffness properties and the intensity of damage in the individual modes are determined. These relationships show that the intralaminar damage reduces all elastic moduli for a general orientation of the damage entities (cracks) and changes the initial orthotropic symmetry of a laminate. The interlaminar damage, however, does not change the symmetry but reduces the moduli. Predictions of the elastic moduli changes are compared with experimental results, showing excellent agreement.     

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF₃/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30)₃/90₂]_s and [(±45)₂/O₂/90₂]_s. Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.